Chi-square tests worksheet with answers

Free printable Chi-square tests worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
colourredgreenblueobserved372914claimed50%30%20%

A sweet manufacturer claims the colour proportions shown in the table. A random sample of 80 sweets gives the observed counts. Compute the chi-square goodness-of-fit statistic χ² for H₀: the claimed proportions are correct.

n = 80k = 3
χ² =
2.Easy
phenotypeA_B_A_bbaaB_aabbobserved169959640claimed9/163/163/161/16

A dihybrid cross is expected to give offspring in the ratio 9 : 3 : 3 : 1. Among 400 offspring the counts shown are observed. Compute the chi-square goodness-of-fit statistic χ² for H₀: the ratio is 9 : 3 : 3 : 1.

n = 400k = 4
χ² =
3.Medium
no defectminormajorTotalday shift424421107night shift17403087Total598451194

The contingency table shows observed counts. For a chi-square test of independence, find the expected count E for the cell “night shift, no defect”.

row total = 87column total = 59N = 194
E =
4.Medium
lowmediumhighTotalurban22452188rural30163076Total526151164

The contingency table shows observed counts. For a chi-square test of independence, find the expected count E for the cell “rural, high”.

row total = 76column total = 51N = 164
E =
5.Hard
dfα = 0.05α = 0.0113.8416.63525.9919.21037.81511.34549.48813.277511.07015.086612.59216.812714.06718.475815.50720.090916.91921.6661018.30723.209

A chi-square goodness-of-fit test compares observed counts in 11 categories with fully specified expected proportions (no parameters are estimated from the data). Using the table, find the critical value χ²crit at significance level α = 0.01.

α = 0.01
χ²crit =
6.Hard
dfα = 0.05α = 0.0113.8416.63525.9919.21037.81511.34549.48813.277511.07015.086612.59216.812714.06718.475815.50720.090916.91921.6661018.30723.209

A chi-square goodness-of-fit test compares observed counts in 3 categories with fully specified expected proportions (no parameters are estimated from the data). Using the table, find the critical value χ²crit at significance level α = 0.01.

α = 0.01
χ²crit =

Answer key

  1. 1. χ² = 1.517
  2. 2. χ² = 34.15
  3. 3. E = 26.46
  4. 4. E = 23.63
  5. 5. χ²crit = 23.21
  6. 6. χ²crit = 9.21

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